Quadrature amplitude modulation (QAM) systems are often utilized where high-speed data communications are required. Typical quadrature amplitude modulation devices are found in satellite communication systems, as well as terrestrial systems, which utilize modems for data communications. In addition, quadrature amplitude modulation circuits can be used in two-way mobile or portable communication systems where digital transmission and encoding techniques are utilized to ensure security of transmissions as required by public service and governmental organizations. Quadrature amplitude modulation systems are desirable because they allow for extremely efficient coding of digital data by encoding digital words comprising multiple data bits onto a modulated signal containing both phase and amplitude information. The data rates of quadrature amplitude modulated signals are limited primarily by the complexity of circuits required both to generate and decode the QAM signals as well as noise and bandwidth characteristics of the transmission media. The field of data communications has grown dramatically in recent years, and, therefore, development of techniques for increasing data transfer rate between devices over existing channels is increasingly important.